Little is known about the beings known as Angels aside from having hobbies like destroying cities and causing worldwide disasters. Fifteen years after the first angel caused the second impact, many more angels began to appear. There are to be 17 in all. One of the unusual things known about the Angels, is that they share all of their genetic makeup with humans. If anyone knows more about them, it's the senior ranking staff at Nerv. But they're not forthcoming about what they know.
Evangelions are the gigantic mecha created to combat the Angels. They may look like some kind of machine, but are in fact biological organisms. They are controlled by a pilot who is inserted into the back of the mecha in a cylindrical tube known as a plug. The plug is filled with a fluid called LCL which directly oxygenates the blood. While they are organisms, they are are electrically powered. This is normally supplied by an external cable (sometimes referred to as the umbilical cord), but can run for about 5 minutes on battery power if the connection is lost.
The biggest concern about the Evangelions (other than their occasional rampage of destruction) is the immense cost of operation and repair. An international treaty was signed, limiting each nation to owning a maximum of two Evangelions in the rebuild. While never stated in the TV series, this does help explain some logic problems with the series.
Fun anime fact: the design of Evangelions in the anime were unpopular with toy manufacturers who thought the design was too complex, and far too difficult to turn into a product. This was possibly intentional.
Pilot: Rei Ayanami
Work on the first prototype Evangelion began a year after the second impact. Unit 0 is the culmination of years of testing, and trial and error. Deep within Nerv headquarters is a creepy looking assortment of body parts that failed to make it into the final prototype. Due to being designed for testing more so than combat, and mental "instabilities" of its pilot, Unit 0 sees the least amount of combat out of the Evas. Unit 0 was painted yellow until nearly destroyed by the 5th Angel. Afterwards the color was changed to blue and shoulder attachments were added.
Pilot: Shinji Ikari
Unit 1 is the test type Evangelion. It's the most complex of the Evangelions, and thus the most expensive. Only adding to the cost problems is Unit 1's good combat record leading it to used more often and thus damaged more often as well. While capable of using a wide variety of weapons and attachments, the main fall back weapon is the "progressive knife". Unit 1 is noted for having the best synchronization with it's pilot, and being fairly dangerous as it's gone out control a few times. It's been hinted that Unit 1 is key to the human instrumentality project and the future of the human race.
Pilot: Asuka Langley Soryu/Shikinami
Unit 2 is the first production type Evangelion, although oddly enough Evas produced after Unit 2 look nothing like it. Parts were produced in Japan, and the unit itself assembled in Germany. As Angel activity is centred around Tokyo 3, Unit 2 is eventually brought back to Japan to fight with the other two Evas. As a production type some parts were simplified probably for cost reasons, but this also seems to have reduced its combat effectiveness slightly as well. Unit 2's primary weapon is the "progressive lance". It is the only Eva with two language settings due to its bilingual pilot.
Pilot: Touji Suzuhara (tv) / Asuka Langley Shikinami (rebuild)
Unit 03 and 04 were built in the United States. After a disaster with Unit 04, the United States transfers Unit 03 to Japan where they're used to Evangelion based disasters. In the TV series, Touji is hastily chosen to be the pilot, and it's revealed that all of Shinji's classmates are pilot candidates for Evas. In the rebuild, Unit 02 is heavily damaged, and Asuka is used to test the Eva while her own Unit 02 undergoes repairs. After activation the Eva is "possessed", and reclassified as the 13th Angel.
Little is known about Unit 04 aside from being built in the United States, so probably very similar to Unit 03. During testing, an explosion causes the entire second branch of Nerv to disappear. Just goes to show, made in the U.S.A. doesn't always mean it's better. (But the black paint job is still bad ass).
Pilot: Mari Makinami
Not much is said about Unit 05 as it's destroyed early on in the second rebuild movie. Unlike the other Evas which are humanoid, Unit 05 has two arms, and four legs with wheels that look like the base of an office chair. The Eva is based in Russia, although it's not explained why a crazy Japanese girl is piloting it - not that anime ever explains why crazy Japanese girls pilot anything.